Fast construction of the Kohn--Sham response function for molecules

Abstract

The use of the LCAO (Linear Combination of Atomic Orbitals) method for excited states involves products of orbitals that are known to be linearly dependent. We identify a basis in the space of orbital products that is local for orbitals of finite support and with a residual error that vanishes exponentially with its dimension. As an application of our previously reported technique we compute the Kohn--Sham density response function ${\chi }_0$ for a molecule consisting of $N$ atoms in $N^2{N}_{\omega }$ operations, with $N_{\omega }$ the number of frequency points. We test our construction of ${\chi }_0$ by computing molecular spectra directly from the equations of Petersilka--Gossmann--Gross in $N^2{N}_{\omega }$ operations rather than from Casida's equations which takes $N^3$ operations. We consider the good agreement with previously calculated molecular spectra as a validation of our construction of ${\chi }_0$. Ongoing work indicates that our method is well suited for the computation of the GW self-energy $\Sigma =\mathrm{i}GW$ and we expect it to be useful in the analysis of exitonic effects in molecules.

References in corpus (6)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Selfconsistent order-N density-functional calculations for very large systems
• Turbo charging time-dependent density-functional theory with Lanczos chains
• The GW space-time method for the self-energy of large systems
• Efficient ab initio calculations of bound and continuum excitons
• On the Kohn--Sham density response in a localized basis set

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